One factor that affects how a given currency's value goes up or down, is the amount of a given currency in circulation, and relative inflation. For instance, if a country begins printing money, the value of a currency is diluted due to inflation, so its value will fall relative to other world currencies. If a large amount of the money supply were somehow burned up, it would have the reverse effect.
Fluctuations Based on Supply and Inflation
Value Changes Based on Demand
Like all markets, currency is affected by both its supply and demand. The desirability, or demand for a given currency also results in changes to its value. The more foreign countries want to hold a certain currency, the more it is worth, and the less they want it, the less it is worth. There are many factors that affect demand for a currency, such as interest rates between countries, political factors, expectations and trade balance. For instance, if you knew a certain country was going to enter a costly war, which might result in the collapse of its government, you would probably want to get rid of any currency you had from that country, and the value of its currency would consequently fall. In general, live exchange rates are a reflection of one currency's desirability versus another at a given point in time.
About Purchasing Power
In a perfect market, the purchasing power of one currency would be the same as another currency. That is, a consumer should be able to purchase the same bundle of goods in one country, that she would be able to by exchanging her money and buying it in another country. This ideal of exchange rates rarely holds true however, for many reasons, such as trade barriers, imperfect competition and prices that do not immediately adjust to reflect a change in a currency's value. This is why traveling to certain countries can seem very cheap, while others can seem expensive. When a currency has greater purchasing power relative to another, that currency is said to be undervalued, while a currency with less purchasing power is said to be overvalued. For instance, if someone buys a hamburger in the United States for $2, and hamburgers in Britain cost 2 pounds, but the person in the United States can only get 1/2 a pound for every dollar, British pounds are overvalued because he can't buy as many hamburgers with pounds in Britain as he can with dollars in the United States.